Control of LPV systems using a quasi-piecewise affine parameter-dependent Lyapunov function

Abstract

This paper presents a new finite-dimensional linear matrix inequality (LMI) formulation for the induced L/sub 2/-norm synthesis of linear parameter-varying (LPV) systems. The approach is based on a nonsmooth dissipative systems theory using a continuous, quasi-piecewise affine parameter-dependent Lyapunov function. The new method is less conservative than previously published techniques based on either affine parameter-dependent Lyapunov functions or robust control techniques. Conservatism is reduced with this new approach because the synthesis uses a very general class of parameter-dependent Lyapunov functions. In contrast to the gridding approach typically used to develop a computationally feasible algorithm, this proposed approach guarantees the synthesis result. We show that the numerical results using our approach, while computationally intensive, can be used to develop many new insights into the potential conservatism of various classes of Lyapunov functions for LPV systems.